- In a class of 20 students, 19 of them took an exam in class and 1 student took a make-up exam the
following day. The professor graded the first batch of 19 exams and found a mean score of 71 points with
a standard deviation of 7.5 points. The student who took the make-up the following day scored 82 points
on the exam.
a) Does the new student’s score increase or decrease the mean score? Give a qualitative argument
without calculations.
b) Formally compute the new mean. Show your work. [For students wanting to play with fancier
equations in R, use $$\frac {numerator}{denominator}$$ to define a fraction. To get a
bar over a letter, use $$\bar x$$. To get a subscript, such as s[x], use $$s_{x}$$. These
various commands can be combined such as $$\bar x = \frac {1+2+3}{3} = 2$$. $$
puts equations on their own line, whereas use $ for inline equations.
c) Does the new student’s score increase or decrease the standard deviation of the scores? Explain.
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